Finite Math Examples

μ = 100

$μ = 100$ ,

σ = 15

$σ = 15$ ,

x = 75

$x = 75$

Step 1

The z-score converts a non-standard distribution to a standard distribution in order to find the probability of an event.

\frac{x - μ}{σ}

$\frac{x - μ}{σ}$

Step 2

Find the z-score.

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Step 2.1

Fill in the known values.

\frac{75 - (100)}{15}

$\frac{75 - (100)}{15}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Cancel the common factor of

75 - (100)

$75 - (100)$ and

15

$15$ .

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Step 2.2.1.1

Rewrite

75

$75$ as

- 1 (- 75)

$- 1 (- 75)$ .

\frac{- 1 (- 75) - (100)}{15}

$\frac{- 1 (- 75) - (100)}{15}$

Step 2.2.1.2

Factor

- 1

$- 1$ out of

- 1 (- 75) - (100)

$- 1 (- 75) - (100)$ .

\frac{- 1 (- 75 + 100)}{15}

$\frac{- 1 (- 75 + 100)}{15}$

Step 2.2.1.3

Factor

5

$5$ out of

- 1 (- 75 + 100)

$- 1 (- 75 + 100)$ .

\frac{5 (- 1 (- 15 + 20))}{15}

$\frac{5 (- 1 (- 15 + 20))}{15}$

Step 2.2.1.4

Cancel the common factors.

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Step 2.2.1.4.1

Factor

5

$5$ out of

15

$15$ .

\frac{5 (- 1 (- 15 + 20))}{5 (3)}

$\frac{5 (- 1 (- 15 + 20))}{5 (3)}$

Step 2.2.1.4.2

Cancel the common factor.

\frac{5 (- 1 (- 15 + 20))}{5 \cdot 3}

$\frac{5 (- 1 (- 15 + 20))}{5 \cdot 3}$

Step 2.2.1.4.3

Rewrite the expression.

\frac{- 1 (- 15 + 20)}{3}

$\frac{- 1 (- 15 + 20)}{3}$

\frac{- 1 (- 15 + 20)}{3}

$\frac{- 1 (- 15 + 20)}{3}$

\frac{- 1 (- 15 + 20)}{3}

$\frac{- 1 (- 15 + 20)}{3}$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

Add

- 15

$- 15$ and

20

$20$ .

\frac{- 1 \cdot 5}{3}

$\frac{- 1 \cdot 5}{3}$

Step 2.2.2.2

Multiply

- 1

$- 1$ by

5

$5$ .

\frac{- 5}{3}

$\frac{- 5}{3}$

Step 2.2.2.3

Move the negative in front of the fraction.

- \frac{5}{3}

$- \frac{5}{3}$

- \frac{5}{3}

$- \frac{5}{3}$

- \frac{5}{3}

$- \frac{5}{3}$

- \frac{5}{3}

$- \frac{5}{3}$